Metro is usually reliable unless there are weather or other emergencies. Traveling Cincinnati's hills in the winter can be difficult. They may have delays and reroutes when Downtown streets are blocked off due to Taste of Cincinnati, Oktoberfest Zinzinnati, Downtown Holiday Dazzle or the occasional parade.
Metro buses may also run late on high traffic days such as the 3rd of the month. Social Security funds are typically distributed then and bus drivers are very attentive to riders who need more time or assistance boarding and exiting.
As to safety, drivers will eject unruly passengers or will phone for police assistance if necessary to keep passengers safe.
The Cincinnati Metro system received a safety award in 2011 as a result of reducing preventable accidents and reinstating safety audits in the maintenance department among other things. Since it has been years since I've ridden a Metro bus, I can't personally speak to its on time reliability; however, I believe that they are fairly reliable within 5-10 minutes of scheduled times. Of course, it areas with more bus routes, the service might be better than in outlying areas with longer distances, more traffic, and less passengers. The main Metro hub downtown, Government Square, recently unveiled a new real-time status boards for the buses, so that you have a better idea of when your bus will be coming. They will also be installing this real-time information at two other locations, as well as including it on their website and offering smartphone apps in 2013.